Write an equation for the cubic polynomial function whose graph has zeroes at 2, 3, and 5. [image 1] Can any of the roots have multiplicity? [image 2] How can you find a function that has these roots?

Answer:

One such function is f(x) = (x − 2)(x − 3)(x − 5) = x³ − 10x² + 31x − 30. None of the roots can have multiplicity greater than 1 because the three distinct roots already account for the cubic’s degree. Write each root as a linear factor and multiply the factors.